Sr Examen
Integral de (x^(4))/(1+x^(1/5)) dx
Solución
Ha introducido
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oo / | | 4 | x | --------- dx | 5 ___ | 1 + \/ x | / 0
$$\int\limits_{0}^{\infty} \frac{x^{4}}{\sqrt[5]{x} + 1}\, dx$$
Integral(x^4/(1 + x^(1/5)), (x, 0, oo))
Respuesta (Indefinida)
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/ | | 4 2 3/5 7/5 9/5 11/5 13/5 17/5 19/5 21/5 23/5 3 4 2/5 4/5 6/5 8/5 12/5 14/5 16/5 18/5 22/5 24/5 | x x 5 ___ / 5 ___\ 5*x 5*x 5*x 5*x 5*x 5*x 5*x 5*x 5*x x x 5*x 5*x 5*x 5*x 5*x 5*x 5*x 5*x 5*x 5*x | --------- dx = C + -- - x - 5*\/ x + 5*log\1 + \/ x / - ------ - ------ - ------ - ------- - ------- - ------- - ------- - ------- - ------- - -- + -- + ------ + ------ + ------ + ------ + ------- + ------- + ------- + ------- + ------- + ------- | 5 ___ 2 3 7 9 11 13 17 19 21 23 3 4 2 4 6 8 12 14 16 18 22 24 | 1 + \/ x | /
$$\int \frac{x^{4}}{\sqrt[5]{x} + 1}\, dx = C + \frac{5 x^{\frac{24}{5}}}{24} - \frac{5 x^{\frac{23}{5}}}{23} + \frac{5 x^{\frac{22}{5}}}{22} - \frac{5 x^{\frac{21}{5}}}{21} - \frac{5 x^{\frac{19}{5}}}{19} + \frac{5 x^{\frac{18}{5}}}{18} - \frac{5 x^{\frac{17}{5}}}{17} + \frac{5 x^{\frac{16}{5}}}{16} + \frac{5 x^{\frac{14}{5}}}{14} - \frac{5 x^{\frac{13}{5}}}{13} + \frac{5 x^{\frac{12}{5}}}{12} - \frac{5 x^{\frac{11}{5}}}{11} - \frac{5 x^{\frac{9}{5}}}{9} + \frac{5 x^{\frac{8}{5}}}{8} - \frac{5 x^{\frac{7}{5}}}{7} + \frac{5 x^{\frac{6}{5}}}{6} + \frac{5 x^{\frac{4}{5}}}{4} - \frac{5 x^{\frac{3}{5}}}{3} + \frac{5 x^{\frac{2}{5}}}{2} - 5 \sqrt[5]{x} + \frac{x^{4}}{4} - \frac{x^{3}}{3} + \frac{x^{2}}{2} - x + 5 \log{\left(\sqrt[5]{x} + 1 \right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.